Basically all you need for turing completeness is the ability to jump/branch/ignore-some-bits on some criteria see SUBLEQ or cyclical tag systems or XY combinat

Basically all you need for turing completeness is the ability to jump/branch/ignore-some-bits on some criteria see SUBLEQ or cyclical tag systems or XY combinators. it's actually very hard to avoid in a system that is supposed to do some sort of computation.